JEE Math Practice Question

Let $$f(x) = \int {{{2x} \over {({x^2} + 1)({x^2} + 3)}}dx} $$. If $$f(3) = {1 \over 2}({\log _e}5 - {\log _e}6)$$, then $$f(4)$$ is equal to

1. A.$${\log _e}19 - {\log _e}20$$
2. B.$${\log _e}17 - {\log _e}18$$
3. C.$${1 \over 2}({\log _e}19 - {\log _e}17)$$
4. D.$${1 \over 2}({\log _e}17 - {\log _e}19)$$